Scattering for the KP-II equation
Abstract
We prove scattering in L2(ℝ2) for real-valued solutions of the Kadomtsev--Petviashvili II (KP-II) equation with localized initial data. No smallness assumption is made, no zero mean condition is imposed, and the admissible data include all Schwartz functions. The proof uses the inverse scattering transform attached to the heat operator. It rests on three ingredients: an a priori bound for the scalar ∂̅ problem which depends on the size of the scattering coefficient but not on its oscillating phase, a nonlinear Plancherel identity proved by analytic continuation from small data, and an estimate showing that the nonlinear part of the reconstruction is negligible on the propagation cones of free waves. To the best of our knowledge, this is the first result establishing scattering for the KP-II equation for every real-valued Schwartz initial datum.
Related
- Global well-posedness and scattering for the defocusing nonlinear Schrödinger equation below energy space
- Strichartz Estimates and Scattering for the Massless Reduced Dirac-Fock Equation
- Threshold Scattering for the Three-Dimensional Focusing Energy-Critical Nonlinear Schrödinger Equation
- Unconditional scattering below the ground state for the three-dimensional focusing energy-critical generalized Hartree equation
- Global well-posedness and scattering for the three-dimensional defocusing cubic Schrödinger equation in Hs, s>1/2
BibTeX
@misc{chen2026scattering,
title = {{Scattering for the KP-II equation}},
author = {Xi Chen},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.13753},
eprint = {2610.13753},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.13753},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Scattering for the KP-II equation
AU - Xi Chen
PY - 2026
DA - 2026/10/13
PB - arXiv
DO - 10.48550/arxiv.2610.13753
UR - https://arxiv.org/abs/2610.13753
AB - We prove scattering in L^2(ℝ^2) for real-valued solutions of the Kadomtsev--Petviashvili II (KP-II) equation with localized initial data. No smallness assumption is made, no zero mean condition is imposed, and the admissible data include all Schwartz functions. The proof uses the inverse scattering transform attached to the heat operator. It rests on three ingredients: an a priori bound for the scalar ∂̅ problem which depends on the size of the scattering coefficient but not on its oscillating phase, a nonlinear Plancherel identity proved by analytic continuation from small data, and an estimate showing that the nonlinear part of the reconstruction is negligible on the propagation cones of free waves. To the best of our knowledge, this is the first result establishing scattering for the KP-II equation for every real-valued Schwartz initial datum.
ER -